Longitudinal functional models with structured penalties

Kundu, Madan G.; Harezlak, Jaroslaw; Randolph, Timothy W.

doi:10.1177/1471082x15626291

Cited by 11 publications

(22 citation statements)

References 37 publications

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“…More recently, there has been interest in analyzing multiple trajectories, with dependencies among the repeatedly measured functional data (Crainiceanu et al, 2009; Di et al, 2009; Kundu et al, 2016; Morris and Carrol, 2009; Morris et al, 2003; Zupinnikov et al, 2011). Functional principal components decompositions for multilevel or longitudinal functional processes have been a major modeling theme in the FDA literature.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Dimensional Functional Principal Components Analysis of EEG Data

et al. 2017

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Summary The electroencephalography (EEG) data created in event-related potential (ERP) experiments have a complex high-dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functional data. The experiments are made up of sequences of multiple trials, resulting in longitudinal functional data and moreover, responses are recorded at multiple electrodes on the scalp, adding an electrode dimension. Traditional EEG analyses involve multiple simplifications of this structure to increase the signal-to-noise ratio, effectively collapsing the functional and longitudinal components by identifying key features of the ERPs and averaging them across trials. Motivated by an implicit learning paradigm used in autism research in which the functional, longitudinal and electrode components all have critical interpretations, we propose a multidimensional functional principal components analysis (MD-FPCA) technique which does not collapse any of the dimensions of the ERP data. The proposed decomposition is based on separation of the total variation into subject and subunit level variation which are further decomposed in a two-stage functional principal components analysis. The proposed methodology is shown to be useful for modeling longitudinal trends in the ERP functions, leading to novel insights into the learning patterns of children with Autism Spectrum Disorder (ASD) and their typically developing peers as well as comparisons between the two groups. Finite sample properties of MD-FPCA are further studied via extensive simulations.

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Section: Introductionmentioning

confidence: 99%

A Multi-Dimensional Functional Principal Components Analysis of EEG Data

et al. 2017

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“…Model (1) was introduced in Kundu et al . () for Gaussian responses; here we extend the framework to accommodate also non‐Gaussian responses that are in the exponential family. For Gaussian responses, our model framework is different from that of Kundu et al .…”

Section: Methodology Proposedmentioning

confidence: 99%

“…For Gaussian responses, our model framework is different from that of Kundu et al . () in the assumptions that are made on the time‐varying effect, γ (·,·). Kundu et al .…”

Section: Methodology Proposedmentioning

confidence: 99%

“…Kundu et al . () assumed that the unknown function γ ( s , t ) has a simple dependence of t but a very complex dependence of s . The unknown function γ ( s ,·) is assumed to be accurately approximated by a linear combination of known temporal functions , which are arbitrarily specified, e.g.…”

Section: Methodology Proposedmentioning

confidence: 99%

“…In their numerical study, Kundu et al . () used two temporal functions f 1 ( t )=1 and f 2 ( t )= t ; the methodology is implemented solely for polynomial temporal functions. In general, it is not clear how to select an optimal temporal basis.…”

Section: Introductionmentioning

confidence: 99%

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Longitudinal Dynamic Functional Regression

Staicu

Islam

Dumitru

et al. 2019

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary The paper develops a parsimonious modelling framework to study the time‐varying association between scalar outcomes and functional predictors observed at many instances, in longitudinal studies. The methods enable us to reconstruct the full trajectory of the response and are applicable to Gaussian and non‐Gaussian responses. The idea is to model the time‐varying functional predictors by using orthogonal basis functions and to expand the time‐varying regression coefficient by using the same basis. Numerical investigation through simulation studies and data analysis show excellent performance in terms of accurate prediction and efficient computations, when compared with existing alternatives. The methods are inspired and applied to an animal science application, where of interest is to study the association between the feed intake of lactating sows and the minute‐by‐minute temperature throughout the 21 days of their lactation period. R code and an R illustration are provided.

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Multilevel modeling of spatially nested functional data: Spatiotemporal patterns of hospitalization rates in the US dialysis population

Nguyen

Banerjee

et al. 2021

Statistics in Medicine

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End-stage renal disease patients on dialysis experience frequent hospitalizations. In addition to known temporal patterns of hospitalizations over the life span on dialysis, where poor outcomes are typically exacerbated during the first year on dialysis, variations in hospitalizations among dialysis facilities across the US contribute to spatial variation. Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multilevel spatiotemporal functional model to study spatiotemporal patterns of hospitalization rates among dialysis facilities. Hospitalization rates of dialysis facilities are considered as spatially nested functional data (FD) with longitudinal hospitalizations nested in dialysis facilities and dialysis facilities nested in geographic regions. A multilevel Karhunen-Loéve expansion is utilized to model the two-level (facility and region) FD, where spatial correlations are induced among region-specific principal component scores accounting for regional variation. A new efficient algorithm based on functional principal component analysis and Markov Chain Monte Carlo is proposed for estimation and inference. We report a novel application using USRDS data to characterize spatiotemporal patterns of hospitalization rates for over 400 health service areas across the US and over the posttransition time on dialysis. Finite sample performance of the proposed method is studied through simulations.

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Longitudinal functional models with structured penalties

Cited by 11 publications

References 37 publications

A Multi-Dimensional Functional Principal Components Analysis of EEG Data

A Multi-Dimensional Functional Principal Components Analysis of EEG Data

Longitudinal Dynamic Functional Regression

Multilevel modeling of spatially nested functional data: Spatiotemporal patterns of hospitalization rates in the US dialysis population

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